M1726471 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	34.5241	69.1176%	3642200	123456789	0.8000	7.9636%	35.3241	71.5770%	2.4593%
PrimeNet	2⁵⁷	0.0111	63.1579%	8000	140000	0.0012	2.7953%	0.0123	64.1877%	1.0298%
GPU72	2⁶¹	0.1779	65.5738%	7000	110000	0.0010	1.3447%	0.1789	66.0367%	0.4629%
Difference	+7	+34.3462	+3.5439%	+3635200	+123346789	+0.7990	+6.6188%	+35.1452	+5.5403%	+5.5403%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1726471	648566394386280607666991	24	79.102	187830086455631345 5 × 11 × 29 × 117761809690051	2020-02-19	29	117761809690051	90,333	504,698	942,635

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-08T16:02:00	Carsten Kossendey	leela	90000	1530000		-		-	-	0.013	-	-	2.095%
2014-04-04T00:13:00	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.008	-	-	0.767%
2014-05-04T12:46:00	Jocelyn Larouche	Manual testing	150000	150000		-		-	-	0.012	-	-	0.970%
2014-10-03T21:04:00	Jocelyn Larouche	Manual testing	187177	187177		-		-	-	0.015	-	-	1.094%
2015-01-09T22:25:00	Jocelyn Larouche	Manual testing	280765	280765		-		-	-	0.022	-	-	1.345%
2015-02-11T12:22:00	Jocelyn Larouche	Manual testing	373697	373697		-		-	-	0.029	-	-	1.541%
2015-02-21T13:42:00	Jocelyn Larouche	Manual testing	411066	411066		-		-	-	0.032	-	-	1.610%
2015-03-08T04:50:00	Jocelyn Larouche	Manual testing	452172	452172		-		-	-	0.036	-	-	1.681%
2015-03-15T18:54:00	Jocelyn Larouche	Manual testing	497389	497389		-		-	-	0.039	-	-	1.754%
2015-04-08T16:59:00	Jocelyn Larouche	Manual testing	601839	601839		-		-	-	0.047	-	-	1.905%
2015-05-01T17:20:00	Jocelyn Larouche	Manual testing	728224	728224		-		-	-	0.057	-	-	2.062%
2015-05-07T16:18:00	Jocelyn Larouche	Manual testing	801046	801046		-		-	-	0.063	-	-	2.144%
2015-05-22T00:28:00	Jocelyn Larouche	Manual testing	881150	881150		-		-	-	0.069	-	-	2.227%
2015-05-26T18:16:00	Jocelyn Larouche	Manual testing	969265	969265		-		-	-	0.076	-	-	2.312%
2015-06-08T13:43:00	Jocelyn Larouche	Manual testing	1066191	1066191		-		-	-	0.084	-	-	2.399%
2015-06-25T21:15:00	Jocelyn Larouche	Manual testing	1172810	1172810		-		-	-	0.092	-	-	2.488%
2015-07-07T18:13:00	Jocelyn Larouche	Manual testing	1290091	1290091		-		-	-	0.101	-	-	2.578%
2015-07-21T01:19:00	Jocelyn Larouche	Manual testing	1419100	1419100		-		-	-	0.112	-	-	2.671%
2015-07-24T22:03:00	Jocelyn Larouche	Manual testing	1561010	1561010		-		-	-	0.123	-	-	2.765%
2015-09-04T18:31:00	mikr	MSI	3642200	123456789		-		-	-	0.800	-	-	7.964%
2018-10-03T11:47:43	Jocelyn Larouche	low 4M	1726471	17264710	12	-		-	-	0.202	-	-	5.311%
2018-10-07T10:38:15	Jocelyn Larouche	low 4M	1726471	69058840	12	-		-	-	0.424	-	-	6.829%
2018-10-12T11:51:00	Jocelyn Larouche	low 4M	1726471	172647100	12	-		-	-	0.868	-	-	7.851%
2018-10-17T22:59:50	Jocelyn Larouche	low 4M	1726471	189911810	12	-		-	-	0.942	-	-	7.959%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-02-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.022	-	-
2016-02-23T16:28:48	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.067	-	-
2010-04-23T13:38:00	Architects Cubed	m1_76l	2⁶⁰	2⁶¹		-	-	0.089	-	-
2016-02-23T16:28:48	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.178	-	-
2010-10-27T20:37:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.924	-	-
2016-02-23T16:28:48	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.569	-	-
2015-05-04T06:23:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.137	-	-
2015-05-04T06:23:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.164	-	-
2015-09-02T13:37:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.328	-	-
2018-04-09T13:44:24	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.657	-	-
2019-06-24T09:36:09	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	17.31	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.226 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	17.226 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		249	17.09
50000	5000000	648566394386280607666991	2	0.137

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-08T21:27:00	Team_Bundu	bundu4	50000	5000000						3	0.206
2009-06-27T09:54:00	James Hintz	11_060902	50000	5000000						3	0.206
2010-07-29T18:26:00	James Classen	towerofart	50000	5000000						3	0.206
2012-01-12T10:54:00	Lukasz Wrobel	WORK_lupo	50000	5000000						3	0.206
2013-05-01T20:55:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2014-01-28T20:23:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2014-11-06T22:23:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2015-07-07T03:37:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2015-12-05T18:55:00	mikr	MSI	50000	5000000						12	0.824
2016-09-22T20:02:45	Bruce	DESK3	50000	5000000						3	0.206
2016-11-22T17:08:11	Bruce	DESK3	50000	5000000						3	0.206
2017-01-16T15:35:16	Bruce	DESK3	50000	5000000						3	0.206
2017-05-12T11:29:19	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2017-12-03T10:50:37	Bruce	DESK3	50000	5000000						3	0.206
2018-02-03T04:33:47	Bruce	DESK3	50000	5000000						3	0.206
2019-07-12T20:19:17	storm5510	7700_Kaby_Lake	50000	5000000						3	0.206
2019-10-31T03:10:41	nordi	nordiputer	50000	5000000						50	3.432
2019-11-18T14:27:37	mnd9	50869	50000	5000000						3	0.206
2020-01-29T08:10:10	EricP	Cannonfodder	50000	5000000						3	0.206
2020-02-15T17:25:45	Alvin Bunk	BADCAT	50000	5000000						3	0.206
2020-02-19T08:03:27	mnd9	kitchen	50000	5000000	648566394386280607666991	79.102	2	2	4912684769096675	2	0.137
2020-05-18T10:38:09	TJAOI	Manual testing	50000	5000000						133	9.128

date	userid	compid	res64	spent (GHz-days)
1999-02-07T00:00:00	ANONYMOUS	v4_computers	CABC0E9A8746686F	0.094
2015-07-18T19:04:00	MadPoo	Manual testing	CABC0E9A8746686F	0.094

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 1726471, B2 = 189911810 (P-1 stage 2)

B1 = 1726471, B2 = 172647100 (P-1 stage 2)

B1 = 3642200, B2 = 123456789 (P-1 stage 2)

B1 = 1726471, B2 = 69058840 (P-1 stage 2)

B1 = 3642200 (P-1 stage 1)

B1 = 1726471, B2 = 17264710 (P-1 stage 2)

B1 = 1726471 (P-1 stage 1)

B1 = 1561010 (P-1 stage 1)

B1 = 1419100 (P-1 stage 1)

B1 = 1290091 (P-1 stage 1)

B1 = 1172810 (P-1 stage 1)

B1 = 1066191 (P-1 stage 1)

B1 = 969265 (P-1 stage 1)

B1 = 881150 (P-1 stage 1)

B1 = 801046 (P-1 stage 1)

B1 = 728224 (P-1 stage 1)

B1 = 601839 (P-1 stage 1)

B1 = 497389 (P-1 stage 1)

B1 = 452172 (P-1 stage 1)

B1 = 411066 (P-1 stage 1)

B1 = 373697 (P-1 stage 1)

B1 = 280765 (P-1 stage 1)

B1 = 187177 (P-1 stage 1)

B1 = 90000, B2 = 1530000 (P-1 stage 2)

B1 = 150000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront